Mathematics 227 (Advanced Calculus II), Spring 2006

MWF 12:00-12:50, MATH 203. Parametrization of curves and surfaces; line and surface integrals; theorems of Green, Gauss, Stokes; applications to physics and/or introduction to differential forms.

Announcements:


Homeworks and other handouts are here.

Study topics and recommended problems.

Tentative schedule:

Textbook sectionsTopicsHours (approx.)
3.1-3.4 Vector-valued functions: Parametrized curves, arclength, curvature and torsion. Vector fields, gradient, divergence, curl, the Del operator. 8
5.5-5.6 Multiple integration: Review of double and triple integrals, change of variables, improper integrals, integration in higher dimensions, applications. 6
6.1-6.3 Line integrals: scalar and vector line integrals, Green's theorem, conservative vector fields. 6
7.1-7.3 Surface integrals and vector analysis: parametrization of surfaces, scalar and vector surface integrals, Gauss's and Stokes's theorems. 8
8.1-8.3 Vector analysis in higher dimensions: introduction to differential forms. 6


Instructor: Dr. I. Laba. Office: Math Bldg 239. Phone: 604 822 2450. E-mail: ilaba@math.ubc.ca.
Office hours: Mon 2-3, Wed 11-12, Fri 2-3. If you cannot come to office hours, please make an appointment in advance. Drop-ins and same-day requests for appointments usually cannot be accommodated.
Textbook: S.J. Colley, Vector Calculus, 3rd ed., Prentice Hall 2005.
Course web page: http://www.math.ubc.ca/~ilaba/math227

Prerequisites: A score of 68% or higher in Math 226, or permission of department head.

Your course mark will be based on the homeworks (20%), two midterms (15% each), and the final exam (50%). Grades may be scaled due to the challenging nature of the course material. Both midterms and the final exam will be strictly closed-book: no formula sheets, calculators, or other aids will be allowed. Academic concession. Missing a midterm, or handing in a homework after the due date, will normally result in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor, or a medical emergency. Supporting documentation (e.g. a doctor's note) will be required. If your request for academic concession is approved, your course mark will be based on your remaining coursework (homework: 20%, midterms and final exam: total of 80%).

Useful links:
[Mathematics Department] [University of British Columbia]